Recovering information about a finite group from its subrack lattice

Kayacan S.

JOURNAL OF ALGEBRA, cilt.582, ss.26-38, 2021 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 582
  • Basım Tarihi: 2021
  • Doi Numarası: 10.1016/j.jalgebra.2021.04.026
  • Dergi Adı: JOURNAL OF ALGEBRA
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.26-38
  • Anahtar Kelimeler: Subrack lattice of a group, Nilpotence class, p-Nilpotence
  • Orta Doğu Teknik Üniversitesi Adresli: Hayır

Özet

We prove that the isomorphism type of the subrack lattice of a finite group determines the nilpotence class. We analyze the problem of estimating the orders of the group elements corresponding to the atoms of the subrack lattice. As a result, we show that the subrack lattice determines p-nilpotence of the group if a certain condition is met. (C) 2021 Elsevier Inc. All rights reserved.